Chapter 12, Problem 18CR

To determine

To find : The measure of an interior angle and the measure of an exterior angle for the regular heptagon.

Answer to Problem 18CR

Therefore, the measure of an interior angle of regular heptagon is ${128.60}^{\circ }$ and the measure of an exterior angle of a regular heptagon is ${51.40}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is regular heptagon.

Formula used : All interior angles of a regular polygon are equal and the measure of an interior angle of regular n-gon is $\frac{\left(n-2\right)\times {180}^{\circ }}{n}$

All exterior angles of a regular polygon are equal and the measure of an exterior angle of regular n-gon is ${180}^{\circ }-\frac{\left(n-2\right)\times {180}^{\circ }}{n}$

Calculation :

Here, polygon is regular heptagon i.e. $n=7$

Therefore, the measure of an interior angle of regular heptagon is

  $\begin{array}{l}\frac{\left(7-2\right)\times {180}^{\circ }}{7}\\ \Rightarrow \frac{5\times {180}^{\circ }}{7}\\ \Rightarrow \frac{{900}^{\circ }}{7}\\ \Rightarrow {128.57}^{\circ }\approx {128.60}^{\circ }\end{array}$

The measure of an exterior angle of a regular heptagon is

  $\begin{array}{l}{180}^{\circ }-\frac{\left(7-2\right)\times {180}^{\circ }}{7}\\ \Rightarrow {180}^{\circ }-\frac{5\times {180}^{\circ }}{7}\\ \Rightarrow {180}^{\circ }-\frac{{900}^{\circ }}{7}\\ \Rightarrow {180}^{\circ }-{128.57}^{\circ }\\ \Rightarrow {51.43}^{\circ }\approx {51.40}^{\circ }\end{array}$